ISSA Proceedings 2010 – Cultural Diversity, Cognitive Breaks, And Deep Disagreement: Polemic Argument

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1. Introduction
Almost every argumentation scholar will be familiar with the famous skit by Monty Python’s Flying Circus called The Argument Clinic (Monty Python 1987; video 2006). A man (played by Michael Palin) comes to the ‘Argument Clinic’, wishing to “have an argument”. After various failed attempts he finally enters the room where an “arguer” (played by John Cleese) offers such service. Yet the argument does not develop the way the client has expected, since when he double-checks that he is in the correct room, Cleese confronts him with a bluntly dishonest statement (“I told you once.”), thereby provoking contradiction from the client, but in the following dialogue confines himself to merely contradicting any statement the client will make. Even when the client tries to define that an argument is not “the automatic gainsaying of any statement the other person makes”, but “a connected series of statements intended to establish a proposition”, and tries to use logic and reason to defeat Cleese, the latter continues to proceed in exactly the same way, until in the end the enervated client rushes out of the room with an exasperated “Oh shut up!”

This sketch makes us laugh, and this is what it is meant to. But what it draws its funny esprit from is the fact that we will all remember having experienced such or similar scenes in reality. Seemingly futile polemic argument appears to be characteristic of our present-day argument culture. TV talk shows confront us daily with disputers yelling at each other and flinging arguments into each other’s faces without ever listening to the other side. And are not today’s political debates more often than not characterized by mere cantankerousness and gain-saying rather than by veritable argumentation? To be honest, even academic discussions oftentimes hardly do any better.

Dissatisfaction with what she feels is a deplorable trait of our Western argument culture provoked Deborah Tannen’s notorious book The Argument Culture (Tannen 1998; 1999). Tannen’s claim is that in our Western societies we argue too much, even when we do not really essentially disagree. In contrast, she advocates a concept of society that would look for common ground rather than dissent and for ‘truth’ rather than debate.

It is easy to see that the little dispute in the Argument Clinic violates each and every one of the pragma-dialectical procedural rules for critical discussion (van Eemeren & Grootendorst 1984, pp. 151-175; 2003; 2004, pp. 135-157) and never gets beyond the confrontation stage. Such an argument that shows no noticeable attempt at resolving the basic dissent by rational means, but consists in nothing but repeated contradiction and gainsaying, we will call a polemic argument.

This paper will try to analyse the preconditions under which and the situations in which such cases of polemic argument are likely, if not bound to occur. In this endeavour, we will make use of the concept of “deep disagreement” developed by Robert Fogelin (Fogelin 1985) and the notion of “cognitive breaks” (“coupures cognitives”) recently identified by Marc Angenot in his book Dialogues de sourds (Angenot 2008, p. 19). It will emerge that deep disagreements typically arise from a lack of common ground between arguers, and that one of the major sources for such a lack and hence for cognitive breaks and deep disagreement is the diversity of the cultural backgrounds of the individual arguers, a problem that rapidly gains in importance in our increasingly multicultural societies. We will determine the sectors and areas in which cultural diversity may manifest itself and the ways in which these diversities may affect the forms, functions, contents, and evaluations of arguments. Based on the theory of antilogical reasoning as a cognitive method developed by the Greek sophists, we will finally seek to establish an underlying logic and rhetoric of purely polemic arguments and to delineate the conditions under which they may still be integrated into a standard of a rational and critical discussion and may play a useful role by helping clarify the issue at stake and the conflicting positions for a broader third-party audience.

2. Common Ground, Deep Disagreement, and Cognitive Breaks
All argumentation necessarily starts from dissent; without any dissent there would be no reason for arguing. But it needs common ground to build on, if it is meant to make any substantial progress. Such common ground is usually provided by a common cognitive, normative, or cultural environment shared by the arguers. The more common ground there exists between the arguers, the better the prospects for a statement to be successful as a speech act and argument. This ‘common ground’ has been described as “shared knowledge” by Ralph Johnson and J. Anthony Blair (Johnson & Blair 2006, p. 77), as “mutual knowledge” or “mutually manifest cognitive environment” by Dan Sperber and Deirdre Wilson (Sperber 1982; Sperber & Wilson 1986), a term also adopted later by Christopher Tindale (Tindale 1999, pp. 101-115), and as “the normative environment the arguers inhabit together” by Jean Goodwin  (Goodwin 2005, p. 111). In the same sense, Michael Billig speaks of “common sense” (Billig 1991, p. 144) and of “communal links, foremost among which are shared values or beliefs” (Billig 1996, p. 226), and Douglas Walton of “common knowledge” (Walton 2001, pp. 108-109) or “general knowledge shared by the speaker, hearer, and audience” (Walton 1996, p. 251).

In a similar way, Aristotle bases the plausibility of dialectical arguments on what he calls endoxa, i.e. generally accepted opinions, which according to a definition he gives in the Topics (1.1, 100b 21-23) is “what is acceptable to everybody or to the majority or to the wise”, as opposed to that which is true by necessity. Aristotle’s notion of endoxa introduces a clearly audience-related element. According to him, arguing is a cooperative cognitive process that happens between arguer and recipient. Accordingly, it is essential that the arguer make sure not only that his or her argument’s premises are adequate, but also in particular that their adequacy is made conspicuous to the recipient (Goodwin 2005, pp. 99 and 111). This cognitive process is clearly enhanced by the extent of common understandings, concepts or ideas shared by both sides.

Yet more often than not such common ground or environment that would ensure successful argumentation is not universal. Values or beliefs arrange themselves into sets of beliefs or belief systems, the importance of which for a correct understanding of the communicative process of argumentation has been emphasized by various theorists (see Gough 1985; Groarke & Tindale 2001; Rescher 2001). Particularly Jim Gough has argued for a view in which such systems of belief “are relative to different individuals in different groups in different contexts” and may thus come into conflict with each other (Gough 2007, p. 499).

Yet in cases in which there is little or no such common ground, argumentation as a communicative process may entirely fail, so that no resolution of the conflict by means of rational argument seems possible. It was for such cases that Robert J. Fogelin first introduced his notion of “deep disagreement” that would be characterized by “a clash of framework propositions” in a Wittgensteinian sense (Fogelin 1985, p. 5). Fogelin distinguishes between two kinds of argumentative exchange: He assumes that “an argumentative exchange is normal when it takes place within a context of broadly shared beliefs and preferences” (p. 3), with which he includes that “there must exist shared procedures for resolving disagreements.” (p. 3). In cases, however, “when the context is neither normal nor nearly normal”, for Fogelin “argument […] becomes impossible,” since “the conditions for argument do not exist.” (pp. 4-5). “The language of argument may persist, but it becomes pointless since it makes an appeal to something that does not exist: a shared background of beliefs and preferences.” (p. 5). In such cases, Fogelin speaks of deep disagreements (p. 5).

A normal reaction to this would be to simply stop arguing. Yet Fogelin seems to be aware of the fact that this is not what normally happens. In most cases, people will nonetheless continue their argument, even though it has become “pointless” since it is bound to fail on a rational level. This gives rise to the question Angenot asks: Why is it that people continue arguing so frantically even though there are obvious “coupures” in their argumentative logic (Angenot 2008, p. 15) and cognition (pp. 17 and 19) that are more or less “insurmontables” (p. 17) and separate arguers from each other to such an extent that they even cannot understand each other’s arguments, since they don’t apply the same “code rhétorique” (p. 15)? Angenot’s ultimate answer is that people do not argue in order to convince anyone, but in order to justify and assert their own position (pp. 439-444) with a certain “imperméabilité” (p. 21). As a consequence, each side will bluntly deny the rationality of the other side’s arguments and declare them plainly absurd, a situation Fogelin describes in terms of “radical perspectivism” (Fogelin 2003, pp. 73-74), which means that “conceptual frameworks” may not only not be shared by opposing parties in an argument (p. 72), but even “wall us off from others enveloped in competing conceptual schemes” (p. 74). If, under such conditions, the argument continues – and it frequently does –, then the result can only be “dialogues of the deaf”, as Angenot calls them, or polemic argument, as we define it (yet not argumentation in the true sense of the word).

Polemic argument, of course, may as well be just wilfully polemic, and the deep disagreement may be faked for provocative purposes without there being any real deep disagreement (as is the case in many TV shows, and oftentimes also in politics). But it may as well be the result of a genuine deep disagreement, as is the case for instance in the debates on abortion, reverse discrimination, the Terri Schiavo case on the removal of life-supporting measures, the debate on separation of francophone Québec from Canada, or dissent on the wars in Iraq and Afghanistan.

Fogelin’s radical and shocking claim that nothing can be done to resolve deep disagreements on a rational level has provoked various reactions from Informal Logicians and argumentation scholars in general. It has been attacked by several scholars: Andrew Lugg (1986) meant to save Informal Logic from this challenge by pointing out that Fogelin’s main examples of the abortion and positive discrimination debates were inappropriate, since in both those cases, in spite of the continuing debate, a perfectly “normal” argumentative exchange was going on. Don S. Levi, too, failed to see how deep disagreements would constitute any limitation on what can be achieved by critical thinking, since in his view the main focus should not be placed on the final verdict about the argument, but on the acquisition of a better understanding of the issues involved (Levi 2000, pp. 96-110). Richard Feldman, while in principle sympathizing with Fogelin’s pessimistic view, argued that “suspending judgment” could be a rational solution, and that consequently there could be no “reasonable disagreement” (Feldman 2005a; 2005b; 2006; 2007). Richard Friemann (2005) suggested that emotional backing could help resolve deep disagreements, and David M. Adams (2005) objected that Fogelin had not specified any a priori conditions that would make a disagreement deep. Yet on the other hand, Fogelin’s thesis has also been defended, among others by Peter Davson-Galle (1992), by Dale Turner and Larry Wright (2005), by Christian Campolo (2005), or by van Eemeren, Grootendorst, Jackson & Jacobs, who do admit that such types of disagreements may mean a serious challenge to the pragma-dialectical model of a critical discussion, since in those cases participants do not enter into the discussion with a resolution-minded attitude, but with very personal interests which each of them regards as privileged and beyond discussion (van Eemeren, Grootendorst, Jackson & Jacobs 1993, pp. 171-72). In a similar way, John Woods has described what he calls “closed-minded disagreements” under the name of “standoffs of force five” (Woods 1992; 1996; 2004, p. 194-199), which he declares intractable; in that respect, he even speaks of “paralysis” and “argumentational blockages” (Woods 1996, p. 650). Moreover, as early as in the fifties, Henry W. Johnstone Jr. had already identified the possibility of “radical conflicts” and “radical disagreement” (Johnstone 1954; 1959, pp. 2-3; 132-133).

3. Cultural Diversity and Deep Disagreement
One of the major factors that may account for diversity of belief systems between arguers, and hence also for deep disagreement, is most certainly the cultural environment each individual has been brought up in or acculturated to. It is only in our globalized and multicultural postmodern world that this obvious fact has become fully manifest, explicably so since culture-specific presuppositions in argumentation frequently remain implicit in terms of unstated premises. In the same sense, Aristotle’s endoxa have also been interpreted as “culturally shared values” vs. topoi as culturally shared rules of inference (Rigotti & Rocci 2005, p. 128).

Whereas culture-specific belief systems may enhance mutual understanding of the argumentative exchange when employed within a cultural community (i.e. when shared by both sides), they are highly likely to create problems in the case of cross-cultural argument. In a cross-cultural argumentative dialogue substantial parts of one arguer’s set of beliefs may not be shared by the other arguer, a fact that may cause incomprehension or misapprehensions. Arguments can thus be culture-specific, culture-determined, and therefore culture sensitive (see Kraus 2010).

Some such notion of cultural sensitivity appears to be addressed by Johnson and Blair, when, in Logical Self-Defense, they define ‘ethnocentrism’ as “a tendency to see matters exclusively through the eyes of the group or class with which one identifies and/or is identified” and declare “most prominent among such groupings […] those by religion, culture, nation, gender, race, and ethnic background” (Johnson & Blair 2006, p. 192). While for Johnson and Blair ‘ethnocentric attachments’ are legitimate, in fact even inevitable, a problem arises whenever they turn into an ‘ethnocentric attitude’, i.e. “one that assumes (probably never explicitly) that our culture is somehow better than others’ culture or else that what is true of our culture is also true of others’ culture.” (p. 192). For Johnson and Blair, an ‘ethnocentric attitude’ is one of the principal causes of fallacious reasoning (p. 192), by reason that it violates the standard of acceptability (p. 58); yet one might as well also say that it may result in a “clash of framework propositions”, which, according to Fogelin, will produce deep disagreement.

“Argumentation is a cultural phenomenon,” says U.S. argumentation educationalist Danielle Endres (2003, p. 293; 2007, p. 381), and she is most certainly right. The study of diversity in argument cultures and of cross-cultural or intercultural argumentation has become a thriving field of global research. But while in earlier times cultural studies searched rather for commonalities between cultures, in recent years, based on empirical field research, the focus has progressively shifted to differences between cultures.

Endres identifies three basic respects, in which arguments may differ across cultural boundaries: forms, functions, and evaluations of argumentation (Endres 2003, p. 294), to which one might wish to add contents. Fogelin, in his analysis, seems to focus on functions and evaluations when he insists that, in a “normal” exchange of arguments, “there must exist shared procedures for resolving disagreements” (Fogelin 1985, p. 3), whereas Angenot appears to concentrate mainly on forms and contents.

The most relevant current approach to cultural diversity is the so-called ‘cultural dimensions approach’, which is “based on the assumption that a culture is best represented by the values and beliefs that a group of people hold in common” (Hazen 2007, p. 7). Its most influential version has been developed by the Dutch scholar Geert Hofstede (1991, 2001). According to Hofstede, cultures can be differentiated on the basis of four value dimensions: 1) individualism vs. collectivism (the degree to which individuals are autonomous from or integrated into groups), 2) power distance (the degree to which people accept or do not accept unequal distribution of power, i.e. hierarchies), 3) uncertainty avoidance (the amount of tolerance for or avoidance of uncertainty and ambiguity), and 4) masculinity vs. femininity (the degree to which gender roles are fixed and respected).

Hofstede’s fairly abstract and generalizing categories are certainly useful, but need to be fleshed out by some material contents. In this respect a taxonomy developed by Barry Tomalin and Susan Stempleski is useful. According to Tomalin and Stempleski, cultures can be defined (and contrasted) by three interrelated elements: 1) ideas (values, beliefs, institutions); 2) products (e.g. customs, habits, food, dress, lifestyle); 3) behaviours (e.g. folklore, music, art, literature) (Tomalin & Stempleski 1993, p. 7).

As far as contents of arguments are concerned, cultural diversity may be said to manifest itself in any one or a combination of the following elements: First and foremost, there are values, norms, codes, and institutions. These may be of religious provenance (including e.g. religious values, beliefs, dogmas, commandments, taboos, views of gender roles etc.), associated with political ideas (e.g. freedom, democracy, legal systems, civil rights vs. hierarchic thinking), or of a more general philosophical and ethical character (e.g. human rights, ethical codes, rules of conduct).

A second group is represented by the elements that form the collective memory of a cultural group, such as the narratives of a society’s myths and history, but also outstanding cultural achievements such as products of literature and art, etc.

A third tier is formed by the standards that regulate everyday social life and interaction, such as language, customs, habits, routines, codes of honour, sense of shame, sense of humour, eating and drinking habits, etiquette, fashion and general lifestyle. With this group would also belong what is called popular culture.

It is easy to see how for instance religious or political values and norms, but also more everyday customs and habits that may enter into an argument as premises may clash in a cross-cultural dispute, so as to create deep disagreement that will not be resolvable as long as the differences in fundamental values are not resolved, which appears not to be feasible by way of rational argument.

As far as functions are concerned, there are cultural communities, such as many Asian or Native American ones, in which the aim of argumentation is not, as in our Western tradition, to win a case against an opponent, but to talk controversial matters over patiently until consensus and harmony can be reached (Endres 2003, p. 294). The focus is on community rather than rivalry and competition.

Forms of arguments and styles and patterns of reasoning, too, may be valued differently in different cultural communities. An argument from authority or expert evidence, for instance, will have a much different effect in communities with high power distance such as most Asian societies, as opposed to communities with low power distance such as Western societies. But even so, a particular authority that is acknowledged by one cultural group need not necessarily be so by another one. This notably applies to religious authorities, as is obvious from the debate on abortion, in which one side claims that abortion is murder since their religion tells them so, which is however declared absurd or non-relevant by their opponents.

Similar discrepancies obtain for arguments from popular opinion (Goodwin 2005, p. 108-109). A statement such as “Everybody thinks that English should be spoken everywhere in the world” may perhaps hold good for the U.S., but other nations may see things differently. Even ad hominem arguments, particularly in their abusive variant, are clearly open to cultural sensitivity, since there is substantial disagreement among different cultures as to what qualifies as a personal affront.

But even a simple argument from example will only work well if the example is known to and acknowledged as such by the interlocutor. Otherwise there will be no common ground to build on, and the argument will go unheard. This applies to all examples taken from a specific cultural group’s collective memory, i.e. from its myths, history or literature. For instance, an argument such as “Non-violence may ultimately prevail, as Gandhi’s example proves” will presuppose some knowledge of modern Indian history.

Evaluation of arguments, finally, is the most delicate point of all. A first issue is relevance. An argument that holds good for one cultural community will appear completely irrelevant to another. For instance, a Native American tribe’s argument that no nuclear waste site should be built on a particular mountain, since that mountain was a serpent lying asleep that would get angry when awakened (Endres 2007, p. 383), was bound to fall on deaf ears with local politicians and engineers. Similarly, the local First Nations’ argument that Mount Uluru (Ayers Rock) in the central Australian outback must not be climbed, because the path crosses an important dreaming track, was bluntly ignored by the Australian Prime Minister, who made access to Uluru for tourists a condition for handing the title to the area back to its original owners.

In a similar way, an argument that would be regarded as sufficient support for a claim in one cultural community, may appear insufficient to a different community. That we must not pollute this planet, since it is God’s creation, might be considered a sufficient argument by devout Christians, but clearly less so in a more secular environment, even if the argument is not considered irrelevant.

Cultural diversity will also strongly affect the strength of arguments. For instance: “You should work more than is requested in your contract, since this is for the best of your company” will be a strong argument in collectivism-oriented cultures such as most Asian societies, but a fairly weak one in highly individualist societies such as most Western ones.

Arguments may even backfire when the addressee, by supplying a contrary premise, interprets them to the contrary of what they were meant to say; or they may unwillingly embarrass or insult the addressee, such as when the former French president Charles de Gaulle defended French colonial policy in Guinea by arguing that France had done many good things to that country, as was amply demonstrated by the perfect French spoken by its president Sekou Touré (Kienpointner 1996, pp. 49-50). De Gaulle’s argument presupposed that francophonization of the colonial population was a positive value. But African anti-colonialists, to whom the argument was addressed, will surely have interpreted this as an expression of cultural imperialism.

Of course, not every argument that is culture sensitive will necessarily produce deep disagreement. According to Danny Marrero, cultural difference in argumentative dialogues comes in three grades: slight, moderate and radical (Marrero 2007, p. 4-6). In dialogues with slight cultural difference, the arguers belong to different groups with minor cultural variations, but still share a clearly defined common ground (p. 4). In a dialogue with moderate cultural difference there is an intersection of the sets of cultural beliefs, but only certain items are shared between the arguers, so that there is only limited common ground (p. 5). In an argumentative dialogue with radical cultural difference, however, there is no common ground at all. “Each arguer has a cultural-specific system of beliefs, values and presuppositions” (p. 5). This is the basis for deep disagreement.

On the other hand, by far not all arguments are culture sensitive at all. Arguments of the type “John should be at home, since there is light in his apartment” or “You should take your coat, since it is raining outside” may qualify as culture-independent. But it can nonetheless be reasonably stated that cultural diversity may be one of the principal causes for deep disagreements.

4. Antilogical Reasoning
At this point, let us for an instant return to the Argument Clinic. When, after minutes of mere gainsaying from the part of his opponent, the client complains that “an argument isn’t just contradiction,” John Cleese retorts: “It can be.” (Monty Python 1987). But can it really? Can mere contradiction in any way be a basis for argumentative resolution of problems?

In that respect, it is helpful to look back some two-and-a-half millennia to the age of the Greek sophists. Those early thinkers had developed a serious method of establishing knowledge by opposition of two contrary statements. This method was to be employed in cases in which certain knowledge was unavailable. Practical examples of this strategy can be found in a judicial context in Antiphon’s Tetralogies (four antilogical speeches in a judicial case; Mendelson 2002, p. 110-112; Tindale 2010, p. 107), in a political context in Thucydides’ pairs of opposed speeches (Mendelson 2002, pp. 103-106; Tindale 2010, pp. 107-108), or in a more philosophical context in the anonymous treatise called Dissoi Logoi (“Opposed speeches”; Mendelson 2002, pp. 109-110; Tindale 2010, pp. 102-104) as well as in Gorgias’s treatise On Not-Being. It was the sophist Protagoras who formulated the axiom that, with respect to any topic, two contradictory statements may be formulated and confronted with each other (frg. B 6a), which became the basic principle of the sophistic technique of antilogia or ‘anti-logic’ (Mendelson 2002, pp. 45-49; Schiappa 2003, pp. 89-102; Kraus 2006, p. 11;).

This theory, however, had a well-defined epistemological foundation (Kraus 2006, pp. 8-9). In his treatise On Not-Being or On Nature, Gorgias advocated the following three statements: There is nothing; even if there were something, it would be unknowable; and even if it both existed and could be known, it could not be communicated to others. Based on such sceptical epistemological views, Gorgias eliminated any reliable criterion of truth. There will be no way of distinguishing a false statement from a true one. All statements will be gnoseologically equal. Hence, since there is no criterion of truth, but only doxa (appearance), any doxa may easily be replaced by another more powerful one by means of logos (speech or reasoning). There is thus, according to Gorgias, always, and necessarily so, a clear cognitive break between individual arguers.

Regarded from this point of view, it is certainly not by accident that all the preferred examples for cases of deep disagreement that are constantly evoked by modern theorists (abortion, positive discrimination, artificial life-supporting measures, political separatism etc.) involve discussions of basic ethical, religious or political values, i.e. topics that typically belong to the realm of doxa (cf. Angenot 2008, p. 46), in which there can be no question of ultimate truth, but both sides may equally claim to have good arguments.

Moreover, it appears that the sophists regarded the ‘art of logoi’ (as they used to tag what was later called rhetoric) basically as an art of combat, as a competition (Kraus 2006, pp. 3-5). Plato, in his dialogue Protagoras (335a 4-8), has Protagoras boast that he would be able to win at any competition of logoi, provided that he was master of the rules; similarly, in the Gorgias (456c 7-457c 2), the sophist from Leontini compares rhetoric with combative sports such as boxing, fencing or wrestling. The pivotal term in all these passages is agṓn, ‘competition’. Also in the Sophist (225a 2-226a 4), as one of the subdivisions of the ‘art of competition’ (agōnistikḗ) there appears the art of ‘arguing contradictorily’, or ‘contradiction’ (antilogikḗ), which then becomes Plato’s standard term for what he thinks is the general sophistic practice of employing logos. This description may not be inappropriate, since references to agṓn, to antilogía, and to combative or competitive arts can be found all over the sophists’ original texts. For instance, the title of one of the most famous works of Protagoras’s, Antilogiai, alludes precisely to the technique described by Plato,

The repeated reference to competition and sports is significant. For sports imply rules and umpires, champions and prizes. The agṓn of logoi which the sophists have in mind is thus more than just mere altercation, it is a well-regulated competition, governed by rules and supervised by impartial umpires, in other words, a formal debate.

In the course of the contemporary turn toward a renaissance of sophistic thinking championed by scholars such as John and Takis Poulakos (J. Poulakos 1983; 1987; 1995; T. Poulakos 1988; 1989), Bruce McComiskey (2002) and others – not to speak of Victor Vitanza’s idea of a modern ‘third’ sophistic (Vitanza 1991) – the technique of antilogical reasoning has been revalued. Michael Mendelson, in a recent book (2002, p. 49), finds in it “the conscious effort to set contrasting ideas or positions side by side for the purpose of mutual comparison”, and he identifies it as a “radically egalitarian” strategy that protects no position as sacrosanct, but, “[i]n giving voice to ‘all pertinent’ logoi, […] creates an opportunity not only for conventionally ‘weaker’ positions to be heard, but, in the juxtaposition of probabilities, for the dominant order to be challenged and even overturned if the alternative case can be made to the satisfaction of those involved.” (p. 56). He thus makes it the root of modern debate.

Nola J. Heidlebaugh, too, in an attempt to tackle the question how, in an age of fractured diversity and pluralism, contemporary society can productively address issues of deep disagreement such as, for instance, the abortion problem, which are considered intractable owing to an “incommensurability” (using Thomas S. Kuhn’s term) of the fundamental conceptions underlying the conflicting positions, draws on the “antithetical method” of the ancient sophists in order to overcome such disagreements by means of an application of classical rhetoric that understands itself as situated, contingent, and practical (Heidlebaugh 2001, pp. 29-48). She observes that, for Gorgias, “the saying of one thing is what makes possible the emergence of its opposite,” and “contradictories emerge as a means of generation in Gorgias’ thought.” (p. 39).

Christopher Tindale, in his most recent book on sophistic argument, devotes a whole chapter to the analysis of antilogical argument. He emphasizes the open-mindedness and fairness of this technique which “sets before the audience a full range of possibilities from which they (and the author) might choose.” (Tindale 2010, p. 110). “Selective biases that favor one perspective over the other” are avoided, so that the audience’s own choice is encouraged and is left completely free and autonomous; there is no advocacy or preference for whatever side (p. 111). Hence, “[n]ot insisting on a truth from among opposing views but working to gain common insights from them is a strength of this approach.” (p. 111).

How might this model help in cases of deep disagreement? Can it help establish an underlying logic of purely polemic argument and delineate conditions under which a standard of a rational and critical discussion may still be maintained?

Maybe the common interest two polemic arguers share in a certain issue already establishes a minimum of common ground that can be built on (see Lueken 1992, p. 283). Maybe even agreement on the fact that there is incommensurability of conceptions and hence the disagreement is intractable may be a rational progress (Lueken 1992, p. 280). The possibility of “reasonable disagreement” (in John Rawls’s sense) in cases of epistemic underdetermination has recently been defended against Feldman’s scepticism (2007) by Marc A. Moffett (2007), Christopher McMahon (2009), and Alvin I. Goldman (2010). With a bit of luck, and some further reflection on both sides, however, even if there is disagreement on a basic level, maybe more common ground can be gained on a higher level, by the “subsumption” of the competing positions under a more comprehensive or overarching problem, by the “elaboration of a more global view which could embody the opposing theses,” as was Chaïm Perelman’s rather optimistic view (1979, p. 115). Other authors have called for more pragmatic solutions by way of “games” of reasoning (“Begründungsspiele”) and “stagings” of situations (“Situationsinszenierungen”) such as “free” exchanges of views (with rational discussion rules temporarily suspended), or learning games (Lueken 1992, pp. 215-347), or by tried and tested methods of classical rhetoric such as commonplaces, topics, and stasis theory (Heidlebaugh 2001, pp. 49-137).

But even if the opponent arguers never gain any common ground themselves, the repeated assertion of their contrary positions, and be it by mere gainsaying, may still help clarify the competing positions for a third party, namely the greater audience that witnesses the dispute. Models for such a view are close at hand. There will always, by definition, be something like deep disagreement between opposing parties or advocates in court or in a political debate, even if this disagreement is sometimes unduly exaggerated or even faked. None of the two parties will accept any of the opponent’s arguments (or pretend not to do so). But the real addressee of their arguments, the one who is really capable of being influenced (see Bitzer 1968) and who will really need to be persuaded, is not the opponent, but the deciding body, i.e. the jury, the assembly, or the electorate. Hence, for instance, a polemic and seemingly aporetic TV debate between politicians of opposing parties may, by forcing the parties to make explicit their positions and arguments, still help the witnessing TV viewer find or better define his or her own position in the controversy.

Possible solutions of situations of deep disagreement by introducing a third party have been advocated earlier, e.g. by Richard Friemann (2001), Vesel Memedi (2007) or Simona Mazilu (2009). We suggest here that, based on the model of the cognitive method of two logoi as developed by the sophists, a rational and critical discussion of issues about which there is deep disagreement may be substantially furthered even by polemic argument, by way of setting out to a broader audience all possible positions in full clarity and in stark contrast so as to enable them to make their choices. For if there really is deep disagreement that cannot be resolved by rational argument, yet decisions must be taken in limited time (as is generally the case for instance in jurisdiction or legislation), such decisions will only be possible by way of deliberate choices that must be made on the basis of an impartial presentation of competing positions. And even if Michael Gagarin may be right in stating that “opposed speeches cannot have the aim of persuading the audience” (Gagarin 2002, p. 30), this may just not be their proper aim; they may well fail in persuading their immediate opponent, but they may nonetheless still help enucleate, highlight, and clarify the essential points in a controversial debate for a third party – the party that makes the ultimate decisions –, and thus lead to a “better understanding of the issues,” as Levi (2000, p. 109) has called for.

5. Conclusion
The above considerations started out from the observation that situations of deep disagreement may arise when common ground between arguers is minimal or non-existent, and when there are cognitive breaks involved, and that, when the argument is continued in spite of that situation, it will turn into merely polemic argument that consists in nothing but contradiction, gainsaying and endless repetition of the same arguments without any substantial move forward.

It was further demonstrated that one of the major sources of such lack of common ground, of cognitive breaks and hence also of deep disagreements may be cultural diversity between arguers that can bring about a clash of basic religious, political, or ethical values that are not considered open to discussion by the parties involved. Since owing to the process of globalization clashes of cultural values are getting increasingly frequent and relevant in processes of argumentation in our present-day multicultural and pluralistic societies, this problem cannot be neglected.

Yet it turned out that, based on the model of the sophistic technique of antilogia, a solution may nonetheless be possible. The model suggests that contrasting arguments can have a cognitive function and may produce insight on a higher level. By making explicit the basic points of disagreement by way of setting them out in contrast, even purely polemic argument may still play a useful role in the rational discussion of controversial issues in a broader public, so that there is after all a way of integrating polemic argument into the rational model of a critical discussion – maybe not for the Argument Clinic, though, for that case is really hopeless.

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